How many ways are there to select five bills from a cash box containing Dollar (1 bills , 2 bills, 5 bills, 10 bills, 20 bills, 50 bills, and 100 bills) ? Assume that the order in which the bills are chosen matters, that the bills of each denomination are indistinguishable, and that there are at least five bills of each type.
In this question, order matters. If ordered had not mattered, then it was a simple stars and bars problem.
How to solve when order matters? Moreover I am not getting the significance of "bills of each denomination are indistinguishable". How is it used here ?
I am getting **C(7,5) * 5^7 **.
Can anyone help here ?
Best Answer
There are 7 options for the first bill you pick. There are 7 options for the second bill you pick, 7 for the third, etc. You pick 5 bills, so the answer is $7 \times 7 \times 7 \times 7 \times 7 =7 ^5=16807$ ways to pick five bills. I hope that this answers your question.